The multiperiodic δ Scuti star 4 Canum Venaticorum: 1997 ... · An analysis of the...

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ASTRONOMY & ASTROPHYSICS MARCH II 1999, PAGE 547 SUPPLEMENT SERIES Astron. Astrophys. Suppl. Ser. 135, 547–553 (1999) The multiperiodic δ Scuti star 4 Canum Venaticorum: 1997 APT photometry M. Breger and F. Hiesberger Astronomisches Institut der Universit¨ at Wien, T¨ urkenschanzstr. 17, A–1180 Wien, Austria e-mail: [email protected] Received November 2; accepted November 30, 1998 Abstract. 204 hours of high-quality measurements of 4 CVn during 32 nights were obtained with the 0.75 m Automatic Photolectric Telescope (APT). The two com- parison stars measured agreed to ±2.7 mmag per single measurement in Stromgren y and ±3.0 mmag in v. It is shown that APT’s can be used successfully for the study of stellar nonradial pulsation at the millimag level. An analysis of the multiperiodicity of 4 CVn revealed the presence of 19 simultaneously excited pulsation fre- quencies. This presents a considerable increase from the 7 frequencies found during a previous campaign of the Delta Scuti Network. The previously known frequencies were confirmed with amplitude variability on a time scale of years. Key words: stars: δ Sct — stars: oscillations — stars: individual: 4 CVn — techniques: photometric 1. Introduction Asteroseismology of δ Scuti stars has reached a stage where the choice between different models of stellar struc- ture and evolution require a large number of known pulsa- tion frequencies. Recent examples of comparisons between observed and modelled nonradial multiple frequencies can be found in Pamyatnykh et al. (1998), Breger et al. (1998), Viskum et al. (1998) and Guzik, Templeton & Bradley (1998). The detection of the frequencies presents a severe challenge to the observers: the most commonly applied method utilizes extensive multisite campaigns, where mil- limag photometric accuracy is obtained. To obtain the required instrumental stability, the Delta Scuti Network adopts the three-star technique (Breger 1993), where mea- surements of the variable star are alternated with those of two comparison stars. The stars are usually changed man- ually at the telescope approximately every 90 s. Send offprint requests to : M. Breger 1.0 1.2 1.4 1.6 0.2 0.1 0.0 k(v) = 0.349 Brightness (mag) Air mass Comparison star 2 k(y) = 0.162 1.0 1.2 1.4 1.6 0.2 0.1 0.0 k(v) = 0.359 Comparison star 1 k(y) = 0.164 Fig. 1. Extinction diagrams for the night of 1997 March 19. The diagram demonstrates the high accuracy with which the extinction coefficients could be determined due to the large number of measurements The conventional technique provides a heavy burden on the observer: the large amount of required data means work of weeks or months at an observatory, which can be quite expensive. Our method of observation with the three-star technique is perfectly suited for an Automatic Photoelectric Telescope (APT), if sufficient accuracy can be obtained without observer intervention. The present

Transcript of The multiperiodic δ Scuti star 4 Canum Venaticorum: 1997 ... · An analysis of the...

Page 1: The multiperiodic δ Scuti star 4 Canum Venaticorum: 1997 ... · An analysis of the multiperiodicity of 4 CVn revealed the presence of 19 simultaneously excited pulsation fre-quencies.

ASTRONOMY & ASTROPHYSICS MARCH II 1999, PAGE 547

SUPPLEMENT SERIES

Astron. Astrophys. Suppl. Ser. 135, 547–553 (1999)

The multiperiodic δ Scuti star 4 Canum Venaticorum: 1997 APTphotometry

M. Breger and F. Hiesberger

Astronomisches Institut der Universitat Wien, Turkenschanzstr. 17, A–1180 Wien, Austriae-mail: [email protected]

Received November 2; accepted November 30, 1998

Abstract. 204 hours of high-quality measurements of4 CVn during 32 nights were obtained with the 0.75 mAutomatic Photolectric Telescope (APT). The two com-parison stars measured agreed to ±2.7 mmag per singlemeasurement in Stromgren y and ±3.0 mmag in v. It isshown that APT’s can be used successfully for the studyof stellar nonradial pulsation at the millimag level.

An analysis of the multiperiodicity of 4 CVn revealedthe presence of 19 simultaneously excited pulsation fre-quencies. This presents a considerable increase from the7 frequencies found during a previous campaign of theDelta Scuti Network. The previously known frequencieswere confirmed with amplitude variability on a time scaleof years.

Key words: stars: δ Sct — stars: oscillations — stars:individual: 4 CVn — techniques: photometric

1. Introduction

Asteroseismology of δ Scuti stars has reached a stagewhere the choice between different models of stellar struc-ture and evolution require a large number of known pulsa-tion frequencies. Recent examples of comparisons betweenobserved and modelled nonradial multiple frequencies canbe found in Pamyatnykh et al. (1998), Breger et al. (1998),Viskum et al. (1998) and Guzik, Templeton & Bradley(1998). The detection of the frequencies presents a severechallenge to the observers: the most commonly appliedmethod utilizes extensive multisite campaigns, where mil-limag photometric accuracy is obtained. To obtain therequired instrumental stability, the Delta Scuti Networkadopts the three-star technique (Breger 1993), where mea-surements of the variable star are alternated with those oftwo comparison stars. The stars are usually changed man-ually at the telescope approximately every 90 s.

Send offprint requests to: M. Breger

1.0 1.2 1.4 1.6

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k(y) = 0.164

Fig. 1. Extinction diagrams for the night of 1997 March 19.The diagram demonstrates the high accuracy with which theextinction coefficients could be determined due to the largenumber of measurements

The conventional technique provides a heavy burdenon the observer: the large amount of required data meanswork of weeks or months at an observatory, which canbe quite expensive. Our method of observation with thethree-star technique is perfectly suited for an AutomaticPhotoelectric Telescope (APT), if sufficient accuracy canbe obtained without observer intervention. The present

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548 M. Breger and F. Hiesberger: APT measurements of the δ Scuti variable 4 CVn

paper reports a successful application of APT technologyto δ Scuti stars.

The variability of the δ Scuti star 4 CVn (HR 4715 =HD 107904 = AI CVn, F3III–IV) was discovered by Jones& Haslam (1966). The discovery was followed by a num-ber of usually relatively short observational studies withcontradictory frequency solutions caused, in part, by thelack of data. During the years 1983 and 1984 a multisitecampaign by the Delta Scuti Network (Breger et al. 1990,Paper I) was carried out at four collaborating observa-tories. This led to the determination of five pulsation fre-quencies which are free of 1 cd−1 alias problems. The anal-ysis of the campaign data together with the previously(mostly unpublished) photometry revealed that 4 CVnpulsates with at least seven frequencies with values of8.59, 7.37, 6.98, 6.19, 5.85, 5.53, and 5.05 cd−1. Theseseven frequencies are independently found and confirmedin different subsets of the 114 nights of photometric datacovering the years 1966 to 1984 (Breger 1990a, Paper II).

Extensive series of unpublished photometry (see Fitch1980) also showed two unusually small frequencies.288 hours of new high-quality observations during a 58-day time span were obtained by Breger et al. (1997) tosolve this question. The two low frequencies of 1.32 and1.40 cd−1 were found to originate in the comparison starused in many studies, HD 108100, which was hereby dis-covered to be a γ Doradus g-mode pulsator.

2. Photometry with the APT

The observations were carried out with one of the two0.75 m APTs located at Washington Camp in Arizona,USA. Since 1996, the twin telescopes named “Wolfgang”and “Amadeus” are the property of the University ofVienna. A detailed description of these telescopes can befound in the paper by Strassmeier et al. (1997). In thispaper it was reported that for variable stars, a photomet-ric accuracy of ±4 mmag in b and y had been achieved.This suggests that with some additional improvement ofthe accuracy, the telescopes could be used for the studyof δ Scuti stars.

The configuration used for the present observationswith the Wolfgang telescope is a Cassegrain system witha focal ratio of f/8. The detector system consists of a800 × 490 pixel CCD used for centering the object. Theactual data aquisition is performed with a blue-sensitivebi-alkali EMI-9124/QB PMT. The water-cooled tube isoperated at a temperature of 3◦C and has a typical darkcount of 20 cs−1.

The outstanding advantage of using an APT for ourthree-star method is the telescope’s speed. The acquisi-tion of the navigation star, which is needed for findingthe actual target group, is performed with a slew speed of10◦ s−1 at a general pointing accuracy of 30 arcsec. Oncethis star has been found, the time needed to slew between

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Fig. 2. Variation of brightness difference between the two com-parison stars (normalized to zero). The error bars are basedon the scatter of the individual measurements within a night.The slow variation is probably a consequence of instrumentalvariations of the APT and not due to small variability of oneof the comparison stars (see text)

the stars of the group and to center the star is about 1 s,which is fast compared to the time the human observerneeds for finding and centering the next object. For thisreason the APT can be regarded as ideal instrument fortime-series photometry, making it possible to obtain morethan 300 separate measurements during a good night.

On the other hand, some problems specific to the APTwere found to exist:

– Difficulties in finding and centering the objects, es-pecially if the weather conditions are not ideal. TheAPT recognizes objects by their brightness. An aver-age brightness value is given and the telescope mea-sures and compares the objects in question with thepreset value. If cloudy or hazy weather influences thebrightness of a star, misidentifications may occur. Suchproblems are, of course, recognized from the data.

– No other stellar object within 0.5 mag (in Johnson B)of the target’s brightness may be in the finder field(about 9 arcmin), as this may make it difficult for thecentering algorithm to choose the correct target.

– Another problem concerns the lack of the clear errormessages coming from the telescopes. This makes ithard for the observer to pinpoint the source of possi-ble problems. For example, the message “Object notfound” could be the result of bad weather, wrong

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M. Breger and F. Hiesberger: APT measurements of the δ Scuti variable 4 CVn 549

Table 1. Journal of the APT measurements of 4 CVn

Date (Beginning) Length C1–C2 residuals Extinction coefficientsUT HJD (245 0000+) hours y (mmag) v (mmag) ky kv

970302 509.720 6.2 2.4 2.5 0.14 0.33970303 510.714 8.0 1.9 2.2 0.12 0.30970306 513.755 6.8 2.9 2.0 0.16 0.35970307 514.705 7.6 2.1 2.7 0.16 0.36970310 517.694 7.1 2.0 2.5 0.18 0.37970311 518.845 4.4 2.7 2.9 0.17 0.36970312 519.757 5.2 2.6 2.6 0.12 0.33

970313 520.722 7.5 (1) 0.16 0.38970314 521.714 7.4 2.7 2.5 0.16 0.34970318 525.674 8.3 2.8 2.7 0.16 0.35970319 526.670 6.2 3.2 2.9 0.16 0.35970320 527.668 8.1 3.1 3.0 0.17 0.36970321 528.680 7.9 2.8 3.0 0.17 0.37970322 529.662 7.6 2.6 2.6 0.14 0.33970324 531.664 7.3 3.2 2.8 0.15 0.33970407 545.618 8.2 2.3 2.3 0.16 0.33970408 546.615 8.3 2.8 3.0 0.17 0.38970409 547.624 6.3 3.2 3.1 0.15 0.24970410 548.625 5.2 2.9 2.9 0.20 0.39970411 549.616 8.1 3.0 2.6 0.19 0.38970412 550.657 7.0 2.1 2.6 0.18 0.37970413 551.617 8.0 2.2 2.4 0.19 0.40970414 552.618 7.8 2.1 2.3 0.17 0.36970415 553.622 7.6 2.6 2.6 0.17 0.36970416 554.673 4.6 2.5 3.1 0.22 0.42970418 556.688 4.2 2.9 3.5 0.17 0.41

970420 558.639 4.7 (1) 3.9 0.16 0.38

970423 561.622 2.5 (1) 2.8 0.28970425 563.623 4.6 2.3 2.8 0.25 0.44970503 571.670 4.0 1.8 2.7 0.15 0.31970505 573.632 6.1 1.9 2.2 0.14 0.31970508 576.633 1.6 2.0 2.1(1) Only comparison star C1 used.

input data to the telescope, technical problems of thetelescope or its steering, or a number of other possiblereasons.

– The present operating procedure of the APT limits themaximum hour angle to 4.2 hours. This means that thelongest set of observations of 4 CVn could only coverslightly more than 8 hours.

These difficulties can be attributed to the operation pro-gram ATIS (Automatic Telescope Instruction Set) con-trolling the telescope. A new, improved version has beendeveloped by NASA engineers and is currently undergoingthe first tests at the APT.

The current limitations of the telescope render it un-usable for certain applications such as observations incrowded fields, since the centering algorithm of the in-strument might become confused. This does not presenta problem for the present program reported in this pa-per. We also note that APT measurements should not beobtained within 30◦ of the Moon.

Between 1997 March 2 and May 8, more than 40 nightsof photometric data of 4 CVn were collected with theWolfgang APT telescope. 4 CVn and two comparison starswere measured through the Stromgren y and v filters. Thedata were reduced in the standard photometric manner.The comparison stars used were HR 4728 (G9III) andHR 4843 (F6IV), for which no variability had been de-tected during previous campaigns. Each observation con-sisted of three single 10-s integrations.

A difference between measurements obtained automat-ically and manually by an observer lies in the handlingof measurements obtained during marginal weather con-ditions. While an observer might stop or attach notesto marginal measurements, the quality of APT measure-ments need to be judged afterwards. This quality con-trol is not available for the present program: instead werejected all measurements for which the standard devia-tion of the three single 10 s integrations was ≥ 10 mmag.Furthermore, all nights or longer fraction of nights during

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550 M. Breger and F. Hiesberger: APT measurements of the δ Scuti variable 4 CVn

509.8 509.9 510.8 510.9 511.0 513.8 513.9 514.0 514.8 514.9 515.0100

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Fig. 3. APT photometry of 4 CVn obtained during the 1997 APT campaign. ∆y and ∆v are defined to be the magnitudedifferences (variable-comparison stars) normalized to zero. The fit of the 19-frequency solutions derived in this paper is shownas a solid curve

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Fig. 4. Power spectrum of the 1997 photometry of 4 CVn. The different panels present the results after prewhitening a givennumber of previously detected frequencies. For the 13 main modes the y and v results are similar so that only y data are shown.For the additional modes, y and v (plotted inverted) data are presented separately at the lower right

which the standard deviation of the C1–C2 measurementswas larger than 4.0 mmag were rejected. We were leftwith high-quality data covering 204 hours during 32 nights(see Table 1). Most of the observing time, which could notbe used or kept after reduction, was due to unfavorableweather conditions rather than equipment problems.

Table 1 also lists the extinction coefficients which werederived from the two comparison stars for each night. Theagreement between the coefficients derived from the twocomparison stars is demonstrated in Fig. 1 for the nightof 1997 March 19. From the residuals of C1–C2 listed inTable 1, it can be seen that the night is of average quality.The data also show a small, systematic variation in extinc-tion between the Eastern and Western hemispheres. Thiseffect can also be seen on a few other nights, but withdifferent signs. Consequently, a systematic East/West ex-tinction difference cannot be demonstrated at this stage.These differences are too small to produce any detectableeffect on the differential photometry of 4 CVn. Wehave also checked the extinction coefficients derived inthis standard way by computing differential extinction

coefficients between C1–C2. The agreement with the val-ues determined in the standard way was excellent.

It might be interesting to look at the average ex-tinction coefficients during the campaign. If we restrictourselves to nights with ≥ 3.0 hours of observation andexclude the night of 970425, which clearly has higherextinction values, the extinction coefficients for theremaining 29 nights show a Gaussian distribution. Thefollowing average values are obtained:

ky = 0.163 ± 0.021, and kv = 0.353 ± 0.037.

These values are typical for the site. Further mea-surements are needed to judge whether or not theobserved variations of the coefficients are significant.

Figure 2 shows that the magnitude difference betweenC1 and C2 exhibits a small, systematic drift over the nineweeks. The drift in v is about twice the amount in y. Themost natural explanation would be small variability of oneof the two comparison stars. Since the third star observed,4 CVn, is not expected to show such slow variability, it

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552 M. Breger and F. Hiesberger: APT measurements of the δ Scuti variable 4 CVn

Table 2. Pulsation frequencies and amplitudes of 4 CVn

Frequency 1997 amplitudes Signal/Noise 1966 – 1984 amplitudes

cd−1 y v y v(1) y

mmag mmag mmag

f1 8.595 17.3 25.9 81 85 11− 23f2 7.375 12.0 18.1 61 62 0− 14f3 5.048 11.6 17.7 58 54 4− 25f4 6.117 10.4 15.8 53 52 Newly grown modef5 5.851 10.3 15.3 52 50 8− 12f6 6.191 5.4 8.3 28 27 0− 6f7 5.532 5.1 8.3 25 26 0− 12f8 6.976 4.9 7.3 25 25 6− 9f9 7.552 4.4 6.1 22 21 New detectionf10 4.749 2.2 3.7 11 11 New detectionf11 6.440 1.9 3.3 10 11 New detectionf12 5.135 1.1 1.6 5.3 4.9 New detectionf13 6.680 1.0 1.5 4.9 4.9 New detectionf14 11.649 1.1 1.7 4.6 5.0 = f4 + f7, new detectionf15 2.327 1.1 1.6 4.2 3.6 = f2 − f3, new detectionf16 1.069 0.9 1.7 3.7 4.1 = f4 − f3, new detectionf17 13.643 0.8 1.5 3.3 4.3 = f1 + f3, new detectionf18 14.712 0.8 1.3 3.3 4.0 = f1 + f4, new detectionf19 12.423 0.7 1.3 2.6 3.6 = f2 + f3, new detection

(1) Amplitude signal/noise limit is 4.00 for newly discovered pulsation modes and 3.50 for “expected” combination frequencies.

should be possible to determine which of the two com-parison stars might be variable. An examination of thezero-point residuals of 4 CVn (after the fits in the nextsection) shows similar drifts in both V-C1 and V-C2, butwith different amplitudes. This suggests an instrumentalorigin of the drifts.

We note the possible existence of low-frequency sta-bility problems of the APT in the millimag range, whichdo not seriously affect the reductions of the much morerapidly varying star 4 CVn. For the reduction of 4 CVn,we have represented the drift between the two compar-ison stars by two different values of (C1–C2) in eachfilter (shown as straight lines in the figure.) The two-week gap in the middle of the observations were causedby poor weather conditions, rather than equipment prob-lems. Consequently, the agreement between the observinggap and the drift maximum is probably accidental. Thepower spectrum of C1–C2 shows a peak of 0.7 mmag at0.036 cd−1 in v and 0.7 mmag at 0.79 cd−1 in y.Consequently, any detected low frequencies in programstars observed with the APT should be checked whetherthey are shown in all filters and relative to all comparisonstars.

The following residuals were found for C1–C2:±2.7 mmag for y and ±3.0 mmag for v per singlemeasurement.

The light curves of 4 CVn are shown in Fig. 3.

3. Multiperiodicity and amplitude variability of 4 CVn

The pulsation frequency analyses were performed witha package of computer programs with single-frequencyand multiple-frequency techniques (programs PERIOD,Breger 1990b; PERIOD98, Sperl 1998), which utilizeFourier as well as multiple-least-squares algorithms. Thelatter technique fits a number of simultaneous sinusoidalvariations in the magnitude domain and does not rely onprewhitening. For the purposes of presentation, however,prewhitening is required if the low-amplitude modes areto be seen. Therefore, the various power spectra are pre-sented as a series of panels in Fig. 4, each with additionalfrequencies removed relative to the panel above. The vand y data give identical results for the first 13 frequen-cies so that only the y results are presented in the leftpanel. For the additional frequencies, we present both they and v (inverted) results in the right panel. Note thatfor the detected frequencies, the amplitude ratio, v/y, isnear 1.5, as expected for these stars. This increases theconfidence that the detected frequency peaks correspondto real pulsation modes, rather than noise artifacts.

One of the most important questions in the examina-tion of multiperiodicity concerns the decision as to whichof the detected peaks in the power spectrum can be re-garded as variability intrinsic to the star. Due to the pres-ence of nonrandom errors in photometric observations andbecause of observing gaps the predictions of standard sta-tistical false-alarm tests give answers which are consideredby us to be overly optimistic. In a previous paper (Bregeret al. 1993) we have argued that a ratio of amplitude

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M. Breger and F. Hiesberger: APT measurements of the δ Scuti variable 4 CVn 553

signal/noise = 4.0 provides a useful criterion for judg-ing the reality of a peak for multisite data. This criterioncan be somewhat relaxed for peaks at previously expectedvalues; viz. harmonics or linear combination frequencies,where a value of 3.5 is adopted. In the present study thenoise was calculated by averaging the amplitudes (over-sampled by a factor of 20) over 5 cd−1 regions centeredaround the frequency under consideration. For the twocombination frequencies below 3 cd−1, smaller intervalsof 1 cd−1 were chosen. The results are shown in Table 2,which also compares the new results to those found by re-analyzing the available data in the literature for the yearsfrom 1966 to 1984.

We noted earlier that the low-frequency terms foundin APT data need to be considered with some caution.For 4 CVn, two low frequencies were detected. We regardtheir reality as quite probable since these peaks do notshow up in the C1–C2 data and the values of the detectedfrequencies match the values calculated from frequencycombinations exactly.

The average deviation of the observations from the fitare 3.0 mmag per single measurement in y and 4.0 mmagin v. This makes it possible to estimate the uncertainties ofthe amplitudes shown in Table 2. Based on the assumptionthat these residuals are random, we can apply the equa-tion σ(a) = σ(m) (N/2)−1/2, where a is the amplitude,σ(m) is the average residual of each data point, and Nthe number of measurements. We derive uncertainties of±0.09 and±0.12 mmag for the y and v amplitudes, respec-tively. Of course, in reality the sources of error are neitherrandom nor independent of frequency (white noise). It isinteresting to note that combining the two y, v data setsdoes not lower the noise level significantly and cannot im-prove the mode detection. Inspection of the data suggeststwo reasons: the computed noise in the frequency regionunder discussion is composed mainly of undetected addi-tional modes and the measuring errors of y and v are notindependent of each other. Although it is not possible toevaluate the errors in more detail, the present calculationcan be useful to estimate whether or not observed ampli-tude variability is real.

4. Additional discussion

The APT measurements have increased the number ofknown pulsation frequencies of 4 CVn tremendously from7 to 19, of which 6 are linear combination frequencies. Allof the previously detected frequencies were confirmed withhigh amplitudes of 5 mmag or more. The newly detectedfrequencies have smaller amplitudes, except for f4, whichhas appeared with a very high amplitude of 10 mmag iny and 16 mmag in v. Although f6 and f4 are separatedby only 0.07 cd−1, the resolution of the older data in theliterature is sufficient to separate the two modes unam-biguously. Inspection of the older data indicates that this

pulsation mode was either not present earlier or had anamplitude of 3 mmag or less.

This growth of a “new” pulsation mode is not unusualfor 4 CVn. The star has a history of slow but steady ampli-tude changes with a time scale of years (see Breger 1990a).Nevertheless, more spectacular changes also occur: from1974 to 1976/7, the high-amplitude mode f2 essentiallydisappeared in order to slowly grow again in amplitudeduring the next decade.

It was shown that the presently available APT is ableto measure at the millimag level. For differences, C1–C2,in the y and v filters, residuals of 2.65 and 3.00 mmagwere found, respectively. 32 nights of data of the δ Scutivariable 4 CVn made it possible to extract 19 simulta-neously excited frequencies with amplitudes as small as1 mmag. The 19-frequency fit of 4 CVn leaves residuals of2.98 and 4.03 mmag. These residuals are slightly higherthan those of the comparison stars and indicate the pres-ence of additional pulsation modes with small amplitudes.The presence of additional, undetected modes is not incontradiction to the excellent fit of the observed and com-puted light curves shown in Fig. 3. The visible light curveis comprised mainly of the modes with large amplitudes,viz. f1 to f8. Large amounts of high-precision data allowthe extraction of additional modes whose detection is sta-tistically significant while not changing the quality of thecomputed light curves to a noticeable degree.

Acknowledgements. Part of the investigation has been sup-ported by the Austrian Fonds zur Forderung der wis-senschaftlichen Forschung, project numbers S7304 and S7301.

References

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and Future Developments (IAU Coll. 136), Butler C.S. &Elliott I. (eds.). Cambridge Univ. Press, p. 106

Breger M., Handler G., Garrido R., et al., 1997, A&A 324, 566Breger M., McNamara B.J., Kerschbaum F., et al., 1990, A&A

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